The decisive role of magnetic anisotropy in honeycomb layered Li 3 Ni 2 SbO 6 and Na 3 Ni 2 SbO 6
J. Werner, W. Hergett, J. Park, C. Koo, E.A. Zvereva, A.N. Vasiliev, R. Klingeler
TThe decisive role of magnetic anisotropy in honeycomblayered Li Ni SbO and Na Ni SbO a, , W. Hergett a , J. Park a , C. Koo a , E.A. Zvereva b , A.N. Vasiliev b,c,d ,R. Klingeler a,e a Kirchhoff Institute of Physics, Heidelberg University, INF 227, D-69120 Heidelberg,Germany b Faculty of Physics, Moscow State University, Moscow 119991, Russia c National University of Science and Technology (MISiS), Moscow 119049, Russia d Russia National Research South Ural State University, Chelyabinsk 454080, Russia e Centre for Advanced Materials, Heidelberg University, INF 225, D-69120 Heidelberg,Germany
Abstract
The decisive role of magnetic anisotropy even in systems with small anisotropyis illustrated for the honeycomb-layered antiferromagnets A Ni SbO with A = Li and Na. Both systems evolve long range magnetic order below T N = 14and 16.5 K, respectively. The magnetic phase diagrams obtained from staticmagnetisation studies up to 15 T imply competing antiferromagnetic phasesand a tricritical point at T N . The phase boundaries are visible in the dynamicresponse of the antiferromagnetic resonance modes, too, which investigationby means of high frequency/high field electron spin resonance enables precisedetermination of magnetic anisotropy. The anisotropy gap amounts to ∆ =360 ± Ni SbO while in Li Ni SbO orthorhombicity is associatedwith ∆ = 198 ± ± T N , the data imply short-rangeantiferromagnetic order up to at least 80 K. The data suggest a crucial role ofanisotropy for selecting the actual spin structure at B = 0 T. Keywords: honeycomb layers, magnetisation, magnetism, anisotropy, phasediagram, electron spin resonance
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Preprint submitted to Advances in Magnetism at the Joint European Magnetic Symposia 2018 (JEMS2018)March 12, 2019 a r X i v : . [ c ond - m a t . s t r- e l ] M a r . Introduction Spin systems realised on layered honeycomb lattices exhibit a variety ofquantum ground states which nature is determined by nearest and next near-est neighbour magnetic interactions. The resulting ground states may be, e.g.,N´eel-, zigzag-, stripe-, and different spiral-type or show spin gaps. [1, 2, 3, 4, 5].While geometric frustration may further affect the ground state spin configu-ration including the complete suppression of long-range magnetic order, alsothe spin size is crucial: while in the spin-1/2 case the particular spiral groundstate [6, 7] can be selected by quantum fluctuations, the spin-3/2 system canshow robust nematic order [8]. Magnetic anisotropy may also play a decisiverole. [6, 9] Honeycomb lattices of A Ni SbO hosting Ni -ions with S = 1provide further insight into this class of layered spin systems. Here, we presentthe magnetic phase diagrams obtained from static magnetisation, specific heat,and thermal expansion studies up to 15 T as well as investigations of the an-tiferromagnetic (AFM) resonance modes by means of high frequency/high fieldelectron spin resonance. Our analysis of the data shows that magnetocrystallineanisotropy can play a decisive role in determining the magnetic properties ofthe materials.
2. Experiment
Polycrystalline A Ni SbO was prepared by conventional solid state synthe-sis as reported previously. [10] For the measurements the sample was pressedinto a pellet with an diameter of ∼ igure 1: (a) Static sus-ceptibility χ = M/B of Li Ni SbO and (b)the derivative ∂ ( χT ) /∂T vs. temperature in exter-nal magnetic fields rangingfrom 1 to 15 T.
3. Results and Discussion
The magnetic field effect on both the static magnetic susceptibility χ = M/B and its derivative ∂ ( χT ) /∂T , in the vicinity of T N , is shown in Fig. 1. Fisher’sspecific heat ∂ ( χT ) /∂T [13] derived from χ ( B = 1 T) shows a sharp anomalyindicating the onset of long-range antiferromagnetic order at T N = 14 K. Thisagrees to the N´eel temperature T N ( B = 0 T) = 14 . B ≥ B , 1.5 to 4 K. At high magnetic fields, onlya step is observed at the high temperature edge of the anomaly, which signals T N ( B ). It has been shown by comparing thermal expansion and magnetisationdata on Na Ni SbO that broadening of the anomaly is associated with thepresence of a transition between two antiferromagnetic phases. To be specific,a shoulder, or rather a second peak, develops at the low temperature edge ofthe anomaly for fields ≤ ∂M ( B ) /∂B , at T = 6 K, is considered(see Fig. 2). The data, at 6 K, suggest three different phases separated byphase transitions at B C1 ≈ B C2 ≈ B C1 appears as a broad peak in ∂M/∂B . In contrast, B C2 isassociated with a kink in the magnetic susceptibility. At T = 4 . B C2 isabove the field range accessible by our experiment. Upon moderate heating,3 igure 2: Magnetic susceptibility ∂M/∂B as a function of the external magnetic field atconstant temperatures for (a) Li Ni SbO and (b) Na Ni SbO . [15] B C1 is only slightly affected while B C2 is considerably suppressed. Though theanomalies are much broader at high magnetic field, the magnetic susceptibilityis reminiscent to the one of Na Ni SbO (Fig. 2b). The magnetisation dataenable constructing the magnetic phase diagram in Fig. 3a. There are threeantiferromagnetic phases which are separated by the phase boundaries B C1 ( T )and B C2 ( T ). As shown above, there is only one distinct anomaly at B = 1 Twhich suggests tricritical points at finite magnetic field as shown in Fig. 3a.Please note larger error bars associated with the anomalies at 2 T ≤ B ≤ Ni SbO (see Fig. 3b) where the AF2 phase extends to B =0 T, yielding a tricritical point at T N . [15] While, the upper critical fields B sat indicating complete suppression of antiferromagnetic spin order is similar in bothcompounds. This implies similar antiferromagnetic exchange interactions whichis corroborated by previously published DFT calculations as well as similarWeiss temperatures. [16]The spin configuration in the AF1 ground state of Li Ni SbO comprises4 igure 3: Magnetic phase diagram of (a) Li Ni SbO und (b) Na Ni SbO [15]. The solidand dashed lines are guide to the eye. The N´eel temperature T N ( B = 0 T) = 14 . Ni SbO was determined by neutron diffraction [14].Figure 4: Resonance frequencies of (a) Li Ni SbO [14] and (b) Na Ni SbO [15] vs. magneticfield. Solid lines represent fits of a two-sublattice AFM resonance model and dashed linesrepresent the high field ω resonance branch . c -direction. [14] Further insight is obtained from anti-ferromagnetic resonance (AFMR) studies by means of HF-ESR as, in the long-range spin ordered phase, HF-ESR is susceptible to the q = 0 magnon modes.The magnetic field dependence of the AFMR resonance frequency of A Ni SbO is shown in Fig. 4. The AF1 spin configuration can be described by means ofa two-sublattice mean field model [14] with uniaxial anisotropy. Fitting theresonances by such model gives the solid lines in Fig. 4. Our analysis yieldsthe anisotropy gaps ∆ = 360 ± Ni SbO as well as ∆ = 198 ± ± Ni SbO . From ∆ ≈ γ B E B A ≈ γ B Sat B A , withthe exchange field B E and the anisotropy field B A , we obtain B A = 1 . Ni SbO and 2.9 T in Na Ni SbO . Anisotropy in Na Ni SbO ismore than two times stronger than in Li Ni SbO which agrees to the observedvalues of B C1 in both systems (see Fig. 3).
4. Conclusions
On the first glance, magnetic phase diagrams in A Ni SbO ( A = Li,Na)seem to be very similar which is consistent to nearly identical magnetic ex-change interactions found by DFT calculations on both systems. [16] However,as shown in Fig. 3, the phase boundaries are clearly different around T N . Thisdifference might originate from a different nature of the AF2 phases in bothmaterials. In Na Ni SbO , AF2 is not a spin-flop phase as can be seen from thesignificant difference of B C1 and the expected spin-flop field. In addition, thereare pronounced structural changes and a sign change of the magnetostriction co-efficient at B C1 which further exclude a bare spin-flop scenario. [15] In contrast, B C1 of Li Ni SbO agrees to the spin flop field expected from analysing theESR phase diagram. Furthermore, the resonance branch ω is well describedin terms of the spin-flop mode (see Fig. 4a). We also note, that the phaseboundary B C1 ( T ) shows very small slope for Li Ni SbO which is typical of aspin-flop transition while in Na Ni SbO there is a strong temperature depen-6ence yielding a tricritical point at T N . In Li Ni SbO , in the vicinity of T N ,i.e., at T = 14 K, B = 3 T is required to stabilize the AF3 phase (not AF2). Weconclude that, in Na Ni SbO , there are nearly degenerated spin configurationsAF1 and AF2 at T N while there is a more conventional spin-flop-like phase inLi Ni SbO which is energetically well separated from AF1.In summary, we have presented the phase diagrams of the quasi-two dimen-sional honeycomb-layered A Ni SbO ( A =Li,Na). While both systems evolvelong range magnetic order, Na Ni SbO shows a tricritical point at T N and thefield-induced AF2 phase is not a bare spin-flop phase. Smaller anisotropy, i.e., B A = 1 . Ni SbO . We conclude a cru-cial role of anisotropy for selecting the actual spin structure at B = 0 T and forthe competition of the three spin ordered phases.
5. Acknowledgements
The authors thank A.U.B. Wolter for valuable support, and V.B. Nalbandyanfor providing the samples for this study. J.W. acknowledges support from theHGSFP and IMPRS-QD. Partial support by the DFG via Project KL 1824/13is gratefully acknowledged. A.N.V. acknowledges support from Russian Foun-dation for Basic Research grant No.18-502-12022. This work was supported bythe Ministry of Education and Science of the Russian Federation in the frame-work of Increase Competitiveness Program of NUST(MISiS)Grant No.K2-2017-084, by act 211 of the government of the Russian Federation, Contracts No.02.A03.21.0004 and 02.A03.21.0011.
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